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Surface Science 604 (2010) 1628–1636 - doi : 10.1016/j.susc.2010.06.006

Published in Elsevier Surface Science

Full field chemical imaging of buried native sub- layers on doped patterns

a b, a a c F. de la Peña , N. Barrett , L.F. Zagonel , M. Walls , O. Renault a Univ Paris-Sud, Laboratoire de Physique des Solides, CNRS/UMR 8502, Orsay, F-91405, France b CEA, IRAMIS, SPCSI, LENSIS, F-91191 Gif-sur-Yvette, France c CEA-LETI, MINATEC, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France

DOI: 10.1016/j.susc.2010.06.006 a b s t r a c t

Fully energy-filtered X-ray photoelectron emission microscopy is used to analyze the Keywords: Semiconductor–insulator interfaces spatial distribution of the silicon sub-oxide structure at the SiO2/Si interface as a Semiconductor–semiconductor thin film function of underlying doping pattern. Using a spectroscopic pixel-by-pixel curve fitting structures analysis, we obtain the sub-oxide binding energy and intensity distributions over the full Silicon field of view. Binding energy maps for each are obtained with a spatial Photoelectron emission resolution of 120 nm. Within the framework of a five-layer model, the experimental Synchrotron radiation photoelectron data are used to obtain quantitative maps of the sub-oxide layer thickness and also their spectroscopy spatial distribution over the p–n junctions. Variations in the sub-oxide thicknesses are Photoelectron emission microscopy (XPEEM) found to be linked to the level and type of doping. The procedure, which takes into account instrumental artefacts, enables the quantitative analysis of the full 3D dataset.

1. Introduction presence of interface dipoles [2,3]. Finally, the width of the photoelectron spectrum may be measured and thus the work function deduced. The original In silicon based micro- and nanotechnologies, the control of the quality reference for synchrotron radiation-based PES studies of this system is the and thickness of the SiO2/Si interface is of prime importance. An interface of work of the Himpsel on Si(100) and Si(111) [4]. Other experimental several atomic layers, with a high defect concentration can result in fixed studies have been carried out by [5,6]. Several models of the interface have charges and contribute significantly to variations in electrical properties. One been proposed in the light of theoretical calculations [7–10]. However, of the limits on CMOS downscaling is the quality of the interface. The typical X-ray spot sizes are of the order of a fraction of a millimetre, therefore of the SiO2/Si interface has already been studied in the laboratory virtually no spatial information is available. Thus, PES is an area-averaged using both angle-resolved X-ray photoelectron spectroscopy (XPS) with Al technique and hence cannot address gate oxide dimensions compatible with K or Mg K X-ray sources and synchrotron radiation-based photoelectron real circuits. Downscaling in microelectronics makes the availability of spectroscopy (PES). The use of XPS to obtain accurate values for the reliable spatially resolved quantification of the interface chemical states a thickness of the SiO2 layer and the sub-oxide interfaces has attained pressing requirement. extremely high standards in order to define a universal method independent of Energy resolved X-ray photoelectron emission microscopy (XPEEM) specific laboratory conditions [1]. The precision now possible in measuring combines the required spatial and resolution. In particular, by oxide layer thickness is smaller than typical variations in silicon bond using soft X-ray excitation combined with a full energy-filtered analysis, lengths. Photoelectron spectroscopy is also non-destructive, allowing elemental, chemical and electronic structure sensitivities of classical PES with complementary analyses such as Secondary mass spectrometry (SIMS) to spatial resolutions on the 100 nm scale are now readily accessible with be performed a posteriori. Synchrotron radiation is particularly useful for a current PEEM instruments. Image series as a function of photoelectron kinetic detailed analysis of the SiO2/Si interface since the depth probed can be energy Ek are acquired step by step over the energy window of interest. Each changed by tuning the photon energy. band PES gives information image gives the intensity as a function of position within the microscope field on the density of states and the valence band offsets, in particular on the of view (FoV). A full image series is a 3D dataset, called a Spectrum Image (SI), allowing extraction of photoemission spectra within the FoV from any area of interest (AOI) down to the pixel size. This technique was first applied in a study of silicon anodic oxidation [11], in which the effect Corresponding author. Tel.: +33 169083272; fax: +33 169088446. E-mail address: [email protected] (N. Barrett).

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2. Experiment

The samples, made in the Laboratoire d'Electronique et de Technologie de l'Information (LETI) at MINATEC, CEA-Grenoble, consisted of two- dimensional doped patterns implanted into silicon in the form of lines with variable spacing and widths from 100m to 0.1m [12]. Before implantation, the silicon wafers were clean and had any surface oxide removed by standard chemical procedures. Each set of lines was identified by figures with the same doping level, giving suitable shapes for optimization of the optics of the PEEM instrument. Two samples were studied, Fig. 1. Phosphor and were used for the n- and p-type doping. The first +/ − + sample, designated N P , had N (representing very high n-type doping) doped zones (1020 cm−3) implanted into a P− substrate (1016 cm−3). The second, designated P+/N, had P+ (representing very high p-type doping) patterns (1020 cm−3) implanted into an N type (1017 cm−3) substrate; the latter was itself deposited on a Si P− wafer (1016 cm−3). A native oxide layer was present on both samples. Fig. 1 also illustrates schematically the expected band line-ups in such samples. The two samples are not symmetric in their preparation since in both cases the starting substrate is P−. Hence, the P+/N sample underwent a supplementary ion implantation to obtain the required doping patterns. The + − doping levels have been measured using secondary ion mass spectrometry Fig. 1. Optical micrograph of doped pattering schematic cross-section of samples N /P and + (SIMS); the results are given in Table 1. P /N. The oxide/substrate and p–n band line-ups are also shown. The spectromicroscopy experiments used a NanoESCA XPEEM system (Omicron Nanotechnology), more fully described elsewhere [16,18]. The of electrostatic charge on the Si 2p emission due to the anodic oxide was apparatus was installed on the CIPO beamline of the ELETTRA synchrotron demonstrated. Using this method, a preliminary analysis of the present system (Trieste, Italy). The incident photon energy was 127 eV, representing the best revealed doping-dependent variations in the overall oxide layer thickness compromise between the beamline undulator response and surface sensitivity. [12]. However, depending on the size of the AOIs up to 99% of the At this energy, the inelastic mean free path (IMFP) of the Si 2p is information in the dataset is not used. low, thus the substrate signal is expected to reflect bent bands at the The most information is available from pixel-by-pixel curve fitting to substrate/oxide interface rather than the flat band situation. Given the depth spectra over the full field. This has already been used in XPEEM analysis to sensitivity, photoelectron diffraction contributions from the substrate are also obtain, for example, concentration maps of InAs/GaAs quantum dots and negligible. The photoelectrons are collected within a 6.1° cone around the rings [13,14]. Ga 3d and In 4d core levels, separated by 2 eV were resolved surface normal. The PEEM contrast aperture diameter was 150 μm, a trade- allowing elemental mapping of the surface. An alternative full field approach off between lateral resolution and PEEM column transmission. The double was developed by Ratto et al. [15], however, it relies on the existence of an internal reference in the sample with known composition, which is not always the case. Furthermore, the information extracted is averaged over the photoelectron escape depth. Such analysis is often, but not always, limited to elemental mapping based on well separated core levels. To accurately map the surface and sub-surface spatial variations in the chemical states and binding energies, careful handling of the dataset and flexible numerical analysis tools are required. One must correct for the microscope transmission function (or illumination) at constant kinetic energy in the FoV, the variations in the photon flux and the non-isochromaticity over the FoV [16,17]. When one does this, the inevitably better statistics gives new quantitative information on the spatial distribution of the chemical states and on sub- surface interfaces. As a test case, we have studied the interface structure of the native oxide as a function of the Si(100) substrate doping. The area- averaged Si 2p core-level studies have already shown that the interface structure is strongly dependent on the particular oxide growth conditions [4,5]. We obtain maps of the SiO2 and the sub-oxide distributions. We show that the SiO2/Si interface is not the same over p- and n-type doped patterns, and develop a model to quantify the spatial extent of the different interface sub-oxides between SiO2 and Si.

Table 1 Doping levels as measured by secondary ion mass spectrometry. 4+ Fig. 2. (a) Non-isochromaticity measurement by a parabolic fit to the Si peak energy as a Sample n-type (at/cm³) p-type (at/cm³) function of the vertical (energy dispersive plane) pixel position in a region far from p–n + − 4+ 20 15 junctions for sample N /P . (b) Si binding energy map obtained from a preliminary fit to the N+/P− 10 1×10 + − Si 2p spectra of sample N /P to a model without correction for the non-isochromaticity and (c) 16 20 + P+/N 2.5×10 10 the same fit corrected for non-isochromaticity. In (b) and (c) the heavily doped N patterns are the bright inverted “L” regions.

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Principal Components Analysis (PCA) [19–21] and blind source separation [22,23] are very promising because they perform the analysis of the full SI

with a minimum of a priori knowledge. However, in their standard form, these techniques assume that the dataset can be represented by a linear model; this is not the case here, since energy shifts are expected as a consequence of the doping level across the FoV. Another approach is to adapt a curve fitting method proposed by Himpsel [4] to the SI. A naive attempt to perform a standard analysis of each spectrum will fail in general due to the following reasons. First, in the kinetic energy range used, the secondary electron emission (SEE) background is non- negligible and cannot be easily accounted for [24]. Second, the lower signal to noise ratio (SNR) of each pixel (with respect to standard PES experiments or AOI spectra) to stability problems in any fitting procedure, Fig. 3. Normalized map of the number of counts of the final model fit at the highest kinetic energy showing no feature which can be associated with the sample structure. This signal is particularly if too many free parameters are used. Third, in the presence of a used as the microscope transmission function. non-negligible SEE background, the standard iterative Shirley background removal cannot be used. Even if the SEE background was negligible or if it hemispherical analyser pass energy of the NanoESCA was 100 eV and 1 mm was removed by other means, the iterative Shirley background cannot be used entrance and exit slits were used. Image series through the Si 2p core level with low SNR [24]. Finally, artefacts such as the non-isochromaticity were acquired in 0.1 eV steps. The overall estimated energy resolution was aberration, the inhomogeneous illumination (or transmission) over the FoV 0.42 eV, with a spatial resolution of 120 nm. All results were taken using a and the synchrotron photon flux decay are all significant for quantitative 25m FoV. In the field of view the heavily doped patterns are the inverted “L” analysis and must be carefully taken into account. shapes. With 4×4 camera binning, the resulting SI has 320×256 pixels and 81 Thus, for accurate results, a curve fitting approach must include careful energy channels. The acquisition time was 3 min per image. The background subtraction and artefact correction. In addition, special attention photoelectron energy E is measured with respect to the sample Fermi level must be given to minimize the number of free parameters in the model and to EF, thus E–EF =EK +ΦWF, where EK is the photoelectron kinetic energy and provide sensible starting values for each pixel. We have defined a six ΦWF the analyser work function. The maximum intrinsic energy dispersion component model: the SEE background, approximated by an exponential or non-isochromaticity in the vertical direction of the FoV is less than 150 function of the form Ae−E/, and five core components to model the core-level 1+ 2+ 3+ meV (see below). The binding energy scale was calibrated using the Fermi emission from metallic silicon and its four oxidation states Si , Si , Si 4+ level and the 3d emission of a flat polycrystalline in situ sputtered Ag sample and Si . Each core component is comprised of the sum of two Voigt curves with the same experimental parameters. with a 2p spin-orbit splitting of 0.61 eV and a branching ratio of 2:1 [4]. The integral of these curves, weighted by a multiplicative factor, s, is added to account for the Shirley background [25,26]. This procedure assures an 3. Data analysis accurate background removal which is essential for quantitative determination of sub-oxides [1]. To correct for the photon flux decay (about 15%), the Although each spatial pixel of the SI obtained by Scanning photoelectron beam current was monitored continuously during the experiment and the microscopy (SPEM) or PEEM contains a standard photoemission spectrum, a intensity of the whole SI was scaled appropriately. quantitative analysis of the full SI involves new challenges. Robust automatic 4 analysis procedures are necessary because there are typically 10 spectra.

+ + − − + − + + + Fig. 4. Full field best fit to the Si 2p spectra averaged over all pixels in a single pattern: (a) N of sample N /P ; (b) P of sample N /P ; (c) N of sample P /N; (d) P of sample P /N.

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+ + − − + − + + + Fig. 5. Best fit to the Si 2p spectra extracted from a single pixel: (a) N of sample N /P ; (b) P of sample N /P ; (c) N of sample P /N; (d) P of sample P /N. The spectra are, of course, noisier than the average spectra of Fig. 4, but the iterative fitting procedure clearly allows extraction of chemical state information pixel by pixel.

The use of hemispherical analyzers in the imaging system naturally of the c parameter as obtained from the non-isochromaticity data of Fig. 2, introduces energy dispersion in one direction of the FoV called non- which in a perfectly aligned optical system should of course indicate the isochromaticity. This has a simple quadratic dependence on position: b× central (binned) CCD pixel. The figure shows that the transmission can be as (Position−c)² [16]. In general, separate experiments must be performed to low as 50% of its maximum, showing the importance of this correction. The measure the non-isochromaticity, however in our case it is possible to fit results were scaled according to this map. determine it with sufficient accuracy from the same dataset. To perform this The fitting procedure was performed as follows. To find suitable starting 4+ measurement, we adjust a parabola to the energy position of Si after a values for each pixel, we first identify differently doped regions by fitting 4+ preliminary fit to the full model, in an area with constant doping, so that any only the most prominent feature of the spectra, the Si peak. We average the energy shift can be attributed to the residual ²-aberration of the imaging SI over the homogeneously doped regions far from the interface and the full spectrometer ( Fig. 2). With this model of the non-isochromaticity we model is fitted to the resulting spectra ( Fig. 4). All the parameters of the construct a map of the energy shift that we apply to all components of the model were free to float at this stage, except the Gaussian FWHM that were 0 1+ 2+ 3+ 4+ model. The average value of these parameters and their standard deviation for fixed to 0.28, 0.44, 0.58, 0.66 and 1.15 eV for Si , Si , Si , Si and Si , + − −5 sample N /P are b= (−7.53±0.30)×10 eV/m and c=(10.38±0.09)m. respectively [4]. The isochromaticity was corrected by aligning the SI Another issue for quantitative microscopy is the non-uniform illumination according to the non-isochromaticity map described above. The total spectral (or transmission function) across the FoV. This can be caused by a vignetting resolution is taken into account by convoluting the Voigt functions with a effect on the lens coupling the scintillator and the image detection system Gaussian representing the instrumental broadening and whose FWHM was (CCD) or by variation of the electron optics transmission function over the free for this fit. The latter converges to 0.5 eV, close to the theoretical energy FoV (at constant kinetic energy). Transmission non-uniformity is measured resolution. The Lorentzian part of the Voigt function represents the lifetime using an image presenting homogeneous photoelectron emission. A first broadening and was found to be 0.2 eV FWHM. The values of the parameters approximation is obtained using the average of the intensity of the last three obtained by fitting the model to the averaged spectra are later on used as images in the high KE end of the SI. After fitting, we use the value of the starting parameters to the pixel-by-pixel fit in the FoV. To ensure a good fit in overall curve fitting model at the highest kinetic energy. The result, shown in all the pixels the chi-squared map is checked after the fit of the full SI and, Fig. 3, is free from any sample-related contrast and is considered to be a good where required, the fit is repeated manually resetting the starting parameters estimation of the transmission properties of the imaging system as a whole until a good fit is reached. Fig. 5 illustrates the fit of the model to individual (electron and light image transmission). The asymmetry in the electron pixels in the differently doped regions. transmission function is possibly linked to the offset observed in the value

0 4+ + − Fig. 6. Binding energy maps for Si to Si obtained from the model based fit to the Si 2p spectra of sample N /P . Energy scales are in eV.

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+ Table 2 region is the heavily doped N zone and the surrounding areas correspond to + − + − Mean binding energies and standard deviations in eV for both N /P and P /N samples. light P substrate doping. Within a given doped pattern the binding energy is constant apart from in the vicinity of a p–n junction, where there are evident + − + Layer N /P P /N changes corresponding to the band line-up. Furthermore, it is an indication of + − + N P N P the accuracy of the non-isochromaticity correction since large areas show the 0 4+ Si 99.24±0.03 99.59±0.09 99.47±0.03 99.57±0.03 same energy across the FoV. In this sense it is illustrative to compare the Si 1+ 0 Si –Si 1.05±0.15 1.08±0.17 1.05±0.29 1.05±0.32 binding energy of Fig. 6 with that of Fig. 2 (a). 2+ 0 Si –Si 1.82±0.12 2.12±0.12 2.13±0.24 2.02±0.24 If one were to consider only the flat band scheme with Fermi level 3+ 0 Si –Si 2.70±0.06 2.87±0.12 2.95±0.16 2.78±0.13 pinning as a function of doping, then the right hand map of Fig. 6, which is 4+ 0 0 Si –Si 4.10±0.01 3.67±0.09 4.00±0.04 4.01±0.04 the Si or substrate emission, is the contrary of what one would expect: highly N-doped Si should pin the Fermi level just below the conduction band A weighted least squares algorithm was used for the fitting procedure. The minimum. However, as already shown [12], the value of the IMFP implies weighting takes into account the Poissonian nature of the noise, and is that the 2p electrons come from bent bands at the oxide interface, and it is the appropriately scaled to account for the corrections applied to the original band bending which significantly modifies the band line-up. In itself this is dataset. All the parameters (i.e. binding energy, intensity and background of not new; what is remarkable is the extent to which the band bending seems each component) were free to float except the FWHM of the Gaussian and spatially homogeneous. Not only does this attest to the quality of the ion Lorentzian of the Voigt profiles and the spectral resolution that was fixed by implantation, but it also validates the extraction of precise values for the band the preliminary fit. The data analysis was performed with HyperSpy [27,28], alignments. The average values of the BE for each chemical state are given in a software suite originally developed for the analysis of EELS spectrum Table 2. 0 1+ 2+ 3+ 4+ images obtained in transmission electron microscopy. HyperSpy is written in Fig. 7 shows the Si , Si , Si , Si , and Si component intensity Python, an increasingly popular scripting language in the scientific maps. The global information obtained from the fit to the average spectra of community, which highly facilitated its adaptation for the present work. The Fig. 4 (a) and (b) is confirmed, but there is considerably more quantitative least squares optimizer used was the Python wrapper around MINPACK's information. We note that the intensities are uniform within a given doping lmdif and lmder algorithms [29] (a modification of the Levenberg– pattern. This is evidence not only for homogeneous ion implantation, as Marquardt algorithm) included in the Scipy scientific library [30]. expected, but also for the accurate correction of the transmission function in the FoV, which would otherwise cause a signal decrease of about 50% from the centre to the edges of the image (see Fig. 3). The chemically resolved Si 4. Results 2p intensity maps will be used as input parameters to a 5 layer model of the SiO2/Si interface in Section 5. 4.1. Si 2p core-level analysis

+ We now present in detail the binding energy and intensity maps resulting 4.1.2. P patterns on N substrate + − + 0 1+ 2+ 3+ from the pixel-by-pixel curve fitting analysis of the samples N /P and P /N. Fig. 8 shows the binding energy maps for the Si , Si , Si , Si and 4+ In both samples, the parameters of the background function, A and τ for Si components. Within a given doping pattern, the binding energy is again the tail of the SSE and s for the Shirley background, are approximately constant. Moreover, sub-oxide binding energies show little or no BE contrast constant for a given doping level. This is a first indication of the homogeneity as a function of doping, in contrast to the sub-oxide binding energy maps of + − of each pattern on the sample and the consistency of the analysis. However, the N /P sample of Fig. 5. Clearly the band line-up is different at the − + going from P to N regions, both A and τ are higher. Given that the general oxide/silicon interface for the two samples. The average BE values of each form of the secondary electron peak must be the same whatever the doping component are given in Table 2. 0 1+ 2+ 3+ and there are no significant direct transitions at ~20 eV from threshold, the Fig. 9 shows the Si 2p intensity maps for the Si , Si , Si , Si and 4+ difference can only be ascribed to an energy difference in threshold, in other Si . The contrast between N-doped and P-doped regions is clearly different + − words, to a shift in the work function. This qualitatively follows the expected from that obtained on the N /P sample shown in Fig. 9. The high contrast 3+ 2+ 1+ + − change in the measured Fermi level position in the gap as a function of observed for the Si , Si and Si sub-oxide intensities on the N /P + doping and surface photovoltage. On the other hand, the change in the Shirley sample is inversed and considerably attenuated on the P /N sample. factor as a function of the doping reflects a change in the loss spectra, and is Table 2 shows the average and standard deviation values for the binding more likely to be linked to the detailed oxide and sub-oxide structure although energies of each chemical state in each doping level. The binding energy its interpretation is out with the scope of this work. shifts from intrinsic Si to silicon oxide are in good agreement with literature + values [4]. We note that the standard deviations for the ensemble of pixel-by- 4.1.1. N patterns on P− substrate 0 1+ pixel spectra are very small and systematically smaller than the overall energy Fig. 6 shows the binding energy maps for the substrate (Si ) and Si , 2+ 3+ 4+ resolution. As a free parameter in our fitting procedure, this confirms the Si , Si and Si , as obtained from the above described fit. The central

0 1+ 2+ 3+ 4+ + − Fig. 7. Si , Si , Si , Si and Si peak area maps obtained from best fits to the Si 2p spectra generated from the N /P SI.

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0 4+ + Fig. 8. Binding energy maps for Si to Si obtained from the model based fit to the Si 2p spectra of sample P /N. Scale is in eV.

4+ accuracy of the results. The correlation of the binding energy results with Si emission also shows high contrast for both samples. Thus, both the sub- band bending requires further analysis as shown in [12] and discussed below. oxide structure and layer thicknesses depend on the doping. The presence of However, in this paper we focus on the structural information provided by the all of the Si sub-oxides indicates that the interface is far from abrupt. Here we thickness model. have evidence of an interface whose extent depends on both the configuration + − + (N /P or P /N) and the doping type and level (n or p). 5. Discussion A quantitative analysis of the extent of the different oxidation states therefore requires a detailed model of the sub-oxide structure. A two-layer The main focus of this paper is the spatially resolved quantification of the model was first proposed by Himpsel et al. [4] and has since been widely sub-oxide thicknesses as a function of the doping level and type of the micron used for two layers. It has been successfully extended to three layers to scale silicon patterns. simulate more complex gate oxide stacks [31]. We use a five-layer model for However, a wealth of information is also available from the binding the sample ( Fig. 10) to calculate the oxide layer thickness using core-level energy distribution as a function of doping. This has already been discussed. intensities. The starting point is to assume that the interface can be 3+ 2+ 1+ Here, we briefly recall the main conclusions [12]. The binding energy of a represented as a stack of five successive layers, SiO2/Si /Si /Si /Si, thus core electron in a doped semiconductor as measured by photoemission using the nearer to the Si substrate, the lower the Si oxidation state. This an intense X-ray source can be written as: assumption agrees with recent angle-resolved Si 2p photoelectron spectra results showing that the sub-oxides are distributed as a function of valence between the Si substrate and the SiO2. [32]. A five-peak model has also been (1) used by Seah [1]. However, in the latter, all of the sub-oxides were assumed to be at the same depth in the oxide stack. This is suitable for an accurate i where BE fb, the binding energy, is measured in the intrinsic case and in determination of the overlying SiO2 thickness, however, we have favoured doping flat band conditions; E F is the shift in the position of the Fermi level the successive stack geometry in order to examine the sub-oxide layer within the gap as a function of doping with respect to intrinsic silicon; EBB is structure. In both cases, the resulting SiO2 should be identical. Here, the the band bending at the substrate/oxide interface; and ESPV is the energy shift major innovation is the application to an entire SI, in order to characterize the due to the surface photovoltage (SPV), which is dependent on both the spatially resolved sub-oxide structure. In other words, the final model is incident photon flux and the substrate electronic structure. adjusted independently with respect to 80 thousand photoemission spectra + − For example, for N /P the measured binding energy is 99.3 eV in the extracted from the 25m FoV. heavily n-doped region, and 99.60 eV in the p-doped substrate. The effect of In the framework of the five-layer model we can write the intensity of the heavy n doping shifts the position of the Fermi level in the gap. With the low signal of each layer as follows: escape depth of the 2p electrons stimulated by the 127 eV incident photons, this is countered by the upwards band bending, which is itself partially flattened by the X-ray induced surface photovoltage. From the calculated SPV values we were able to estimate the real band bending at the oxide/substrate where Si indicates the layer of i oxidation state. is the interface [12]. attenuation of the electrons in the layer due to an IMFP Layer, dLayer is the Now we turn to the extraction of the sub-oxide thicknesses as a function  thickness and I Layer is the intensity from semi-infinite blocks with the same of position in the microscope FoV. We can obtain qualitative information composition as the layer. This intensity is given by: about the oxides from the rich structure of the intensity maps of the Si core- 0 level components ( Figs. 7 and 9). For both samples the Si emission from the n-type region is higher than from the p-type region, indicating a thicker oxide 2+ layer for the latter. There is high contrast in the Si valence state for the n being the Si atomic density and  the photo-ionization cross- + − + Layer Layer N /P sample, whereas, for the P /N sample the contrast is much lower. The section.

0 1+ 2+ 3+ 4+ + Fig. 9. Si , Si , Si , Si and Si peak area maps obtained from best fits to the Si 2p spectra generated from the P /N SI.

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The total sub-oxide thickness is 0.42 nm, three quarters of which can be 3+ attributed to the Si rich layer. Therefore the interface, mainly composed of 1+ 2+ − Si and Si , appears sharp. In contrast, the oxide over the P doped regions − is thicker, 2.19 nm. The total sub-oxide thickness over the P regions is + almost three times that over the N zones and there are marked differences in the thicknesses of each sub-oxide as a function of doping. The SiO2 decreases by 0.26 nm whereas all of the sub-oxide thicknesses increase. The most 2+ spectacular change is that of the Si layer, which increases by 0.43 nm. Since Si–O bond lengths are typically 1.6–1.8 Å, the extended interface associated with Si in the 2+ oxidation state must be two to three atomic layers − 2+ thick over the P pattern. The presence of a distinct Si sub-oxide layer over Si(100) was also reported by Rochet et al. [5], although much thinner, probably because they grew a thermal oxide in vacuum, rather than studying + the native oxide as in our case. In contrast, the P /N sample presents a total + Fig. 10. Schematic of the five-layer model: each layer corresponds to a different chemical state oxide thickness of 1.49(1.64) nm over the N(P ) regions, mainly due to the 0 1+ 2+ of silicon, going from the substrate (bulk silicon, Si ), through the sub-oxides (Si , Si , and 3+ 4+ SiO2 layer, whereas the sub-oxide thicknesses are almost constant. Si ) to the surface (silica, Si ). The thicknesses of each zone and layer are best summarized by considering the mean values and their standard deviations in each differently doped region far from the interface. The results are shown in Table 4. The Dividing the equations for 1 ≤i ≤4 by the substrate signal intensity ISi°, we can obtain a set of 4 equations from which the thickness d of each layer can standard deviation for the measured thickness is significantly smaller than typical Si–O bond lengths, which suggests that the model of five distinct be calculated recursively: 2+ layers is reasonable. The exception is the standard deviation in the Si + + − thickness over the N region of the N / P sample which is about the same as 2+ + the thickness obtained for the Si layer of the P /N sample. This is partly due to the low intensity of the sub-oxide component, however, other low 2+ For each silicon oxidation state the ratio of the semi-infinite intensities to intensity components give smaller standard deviations. Thus, the Si layer 0 that of Si at hν=127 eV photon energy is required. Each of these ratios is probably has significant atomic roughness and a high concentration of the product of three ratios: the Si atomic densities nLayer/nSi, the IMFPs defects. The expected variations in silicon–oxygen bond lengths are much Layer/Si and the photo-ionization cross-sections Layer/Si. Following smaller, for example, Giustino and Pasquarello [33] showed that the Si–O 3+ 4+ Himpsel [4], there is a near 130 eV for Si and Si , we have bond length could only vary by up to ±0.005 nm. therefore interpolated the cross-section values given for 120 and 130 eV, and Across the p–n junctions in both samples, the spatial variation of the 3+ 4+ assumed that the Si cross-section scales in the same way as Si , obtaining thickness of the different layers is smooth, which is an extra indication of SiO²/Si = 2.08 and Si³+/Si =1.6. The atomic silicon concentration in SiO2 the quality of the analysis. By fitting an error function to the curve of the 22 −3 22 −3 is nSiO² =2.2×10 at/cm and in silicon nSi =5.0×10 at/cm . For the Si0/Si+ interface for both samples we can estimate the spatial extent of intermediate oxides we assume that the concentration scales with the valence the thickness change across the junction. The presentation in Fig. 13 state. We use an IMFP of 0.7 nm for silicon oxide and 0.33 nm for the Si shows a slightly wider depletion region in the P+/N sample. substrate [31], the IMFPs in the sub-oxide layers are interpolated linearly The width over which the sub-oxide structure changes at the p–n junction + − with the oxidation state. The parameters are given in Table 3. is smaller in the case of the N /P sample than the expected depletion width, + Using this model, the thickness of the SiO2 and each sub-oxide layer can whereas in the case of the P /N sample it is larger. One reason may be that 1+ be calculated from the intensities associated with the respective components the width as measured here depends on the statistics associated with the Si in the Si 2p spectrum at each pixel of the whole dataset. Hence, oxide and emission, which is considerably attenuated, however, this is to a large extent sub-oxide thickness maps can be obtained as shown in Fig. 11 (a) and (b). compensated by the full field analysis, as can be inferred from Figs. 4 and 5. To illustrate thickness variations across the different doping levels Fig. 12 The reason might be intrinsic to p–n junctions. The band alignment will shows the oxide and sub-oxide thickness profiles along a line of length 6.1m generate a local lateral electric field which can considerably alter the perpendicular to the p–n junctions. An alternative presentation is shown in trajectories of the photoelectrons [34]. The field will be directed from the n- Fig. 13 which stacks emphasizing the topography of the buried interface. to p-type regions; however its actual magnitude will depend both on the The oxide layer is always thicker over the p-doped regions than over the n- Fermi level position and the depletion width, which are clearly different for + − + doped regions. Secondly, it is thicker on the N /P sample than on the P /N the two samples. For a p–n junction between heavily doped n-type silicon and sample, whatever the doping. In the former, over the heavily n-doped regions the lightly doped p-type silicon, the band offset is about 1 eV and the depletion native oxide has a total thickness of 1.76 nm, of which 1.34 nm is due to SiO2. width of the order of 1m. This will induce a lateral electric field of ~1 kV/mm, significant with respect to the 7 kV/mm of the extractor lens. Thus, in the region of the junction the photoelectron trajectories will be bent Table 3 by the lateral electric field, and the junction position and even width in the Estimated photoemission parameters for Si 2p electrons at 127 eV photon energy, used in the model of the Si 2p core-level component intensities. PEEM images may not correspond to the real values. We have tried several extractor lens voltage settings in order to vary the nominal lateral resolution ∞ ∞ Layer Layer/Si Layer/Si nLayer/nSi I Layer/I Si between 150 and 70 nm. At threshold, i.e. for very low kinetic energies, we 1+ Si 1 1.28 0.86 1.10 2+ were unable to improve the measured resolution across the junction below Si 1.10 1.56 0.73 1.25 105 nm. Thus, we believe that the lateral electric field in the vicinity of the Si3+ 1.60 1.84 0.59 1.74 4+ Si 2.08 2.12 0.46 2.03 junction limits the resolution to 100 nm.

F. de la Peña et al. / Surface Science 604 (2010) 1628–1636 doi : 10.1016/j.susc.2010.06.006 F. de la Peña et al. / Surface Science 604 (2010) 1628–1636, doi : 10.1016/j.susc.2010.06.006 1635

+ − + Fig. 11. Oxide and sub-oxide thickness maps for (a) sample N /P and (b) P /N derived from the five-layer model of Fig. 10. Thickness scale in nm.

+ For the higher KE Si 2p electrons, this figure should represent an upper over the P doped region. As explained above, the latter sample required limit. We have checked the surface topography of the native oxide using successive P and B implantation, thus the regions cannot be simply compared AFM. The doped patterns are systematically higher than their respective to macroscopic doped silicon wafers. Using Vegard's law as a first + − substrates. The height differences are 1 nm for the N /P sample and 0.5 nm approximation and assuming that the post implantation annealing was + for the P /N sample. These differences are introduced during ion sufficient to produce a homogeneously doped layer we can estimate the strain implantation. They do not change the sub-oxide thicknesses as deduced from induced in the Si substrate by doping [37], however, the resulting isotropic 4+ 3+ photoemission. The structure visible in the Si and Si thickness maps in strains for the two samples are less than 0.01%. The differences in the oxide Fig. 11 (a) is possibly due to such topography. However, to incorporate the growth are therefore more likely to be due to electrical enhancement of the AFM topography into Fig. 13 requires knowledge of the positional shifts due oxidation. Finally, charging of SiO2 overlayers is also known to affect the to the lateral electric field across the junction. Once this is done, it will be measured binding energy, however, this only becomes significant for oxides possible to describe the full surface and sub-surface topographies by a thicker than about 2 nm [38]. Furthermore, we have measured no time combined and non-destructive XPEEM–AFM analysis. The effect of the dependence of the binding energy, suggesting that charging in these films is lateral electric field is therefore of general relevance to PEEM imaging of negligible. semiconductor structures and is currently under study.

Two other possible effects in photoemission need to be considered. 6. Conclusion Exposure for several hours to high intensity soft X-ray radiation can induce room temperature desorption of semiconductor oxides. Heun et al. We have used full field energy-filtered photoelectron emission demonstrated this in the case of SiO2 [35]. However the brilliance of the microscopy to analyze the spatial variation of the binding energies and X-ray source used by them was three to four orders of magnitude higher thicknesses of the native oxide layers on p- and n-doped micron scale silicon than that on the CIPO beamline used in these experiments. Thus we can patterns. Using a pixel-by-pixel spectral analysis and by correcting for non- exclude radiation induced thinning of the native oxide in our results. A isochromaticity, microscope transmission functions and synchrotron photon comparative study of the oxide formation on Si(100) for equivalent B or flux decay, quantitative information is made available. From a five-layer P doping profiles has shown a faster SiO2 growth on n-doped silicon than model for the Si 2p core-level intensities we can deduce the variations in the + − on p-doped silicon [36]. This is what we observe for the N /P sample. extent of the different oxide layers. Both samples are thicker in the p-doped + + − On the other hand, for the P /N sample we observe a thicker SiO2 layer areas, the N /P sample presenting a total variation in thickness two

Fig. 12. Thickness profiles for each silicon oxidation state. In this figure, the profiles display the thickness of each layer independently.

F. de la Peña et al. / Surface Science 604 (2010) 1628–1636 doi : 10.1016/j.susc.2010.06.006 1636 F. de la Peña et al. / Surface Science 604 (2010) 1628–1636

Table 4 Mean value and standard deviations for oxide and sub-oxide layer thicknesses in nm for + − + N /P and P /N samples. Layer N+/P− P+/N N+ P− N P+ Si0 – – – – Si1+ 0.05±0.02 0.19±0.03 0.04±0.01 0.03±0.01 Si2+ 0.06±0.03 0.49±0.06 0.10±0.02 0.07±0.02 Si3+ 0.31±0.06 0.43±0.05 0.24±0.04 0.23±0.03 Si4+ 1.34±0.03 1.08±0.06 1.11±0.05 1.31±0.04

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